Things outside of Egypt have been very different over the last 1500 years. In a context of the complete domination of the country by Islam it makes sense that only the Churches kept the relics safe, and in any case, being rather cut off, there was little reception of other relics, or the sending of relics to other places.
In the West there has not been the same situation and so relics were much more available from place to place and were shared with churches in different countries. This much greater availability meant that first of all the most important nobility might be given some small relic, and then other laity also had the opportunity to acquire small relics.
If the West had been oppressed in the same way then the access to relics would undoubtedly have been as restricted as it has been in Egypt. In the West many laity, priests and of course Churches, have access to relics and it is not considered desperately unusual.